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2017 A single-stage flux-corrected transport algorithm for high-order finite-volume methods
Christopher Chaplin, Phillip Colella
Commun. Appl. Math. Comput. Sci. 12(1): 1-24 (2017). DOI: 10.2140/camcos.2017.12.1

Abstract

We present a new limiter method for solving the advection equation using a high-order, finite-volume discretization. The limiter is based on the flux-corrected transport algorithm. We modify the classical algorithm by introducing a new computation for solution bounds at smooth extrema, as well as improving the preconstraint on the high-order fluxes. We compute the high-order fluxes via a method-of-lines approach with fourth-order Runge–Kutta as the time integrator. For computing low-order fluxes, we select the corner-transport upwind method due to its improved stability over donor-cell upwind. Several spatial differencing schemes are investigated for the high-order flux computation, including centered-difference and upwind schemes. We show that the upwind schemes perform well on account of the dissipation of high-wavenumber components. The new limiter method retains high-order accuracy for smooth solutions and accurately captures fronts in discontinuous solutions. Further, we need only apply the limiter once per complete time step.

Citation

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Christopher Chaplin. Phillip Colella. "A single-stage flux-corrected transport algorithm for high-order finite-volume methods." Commun. Appl. Math. Comput. Sci. 12 (1) 1 - 24, 2017. https://doi.org/10.2140/camcos.2017.12.1

Information

Received: 4 May 2015; Revised: 13 January 2017; Accepted: 18 January 2017; Published: 2017
First available in Project Euclid: 19 October 2017

zbMATH: 1362.65091
MathSciNet: MR3652438
Digital Object Identifier: 10.2140/camcos.2017.12.1

Subjects:
Primary: 65M08

Rights: Copyright © 2017 Mathematical Sciences Publishers

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Vol.12 • No. 1 • 2017
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